If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value o

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Question: If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value of k?

Options:

Correct Answer: 10

Solution:

Using the sum and product of roots: -2 + -4 = -6 and -2*-4 = k => k = 8.

If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value of k?

If the roots of the equation x^2 + 6x + k = 0 are -2 and -4, what is the value of k?

Step 1: Identify the given quadratic equation, which is x^2 + 6x + k = 0.
Step 2: Note the roots of the equation, which are -2 and -4.
Step 3: Use the formula for the sum of the roots. The sum of the roots is -2 + -4.
Step 4: Calculate the sum: -2 + -4 = -6.
Step 5: According to the quadratic formula, the sum of the roots (which is -6) should equal -b/a. Here, b = 6 and a = 1, so -b/a = -6.
Step 6: Now, use the formula for the product of the roots. The product of the roots is -2 * -4.
Step 7: Calculate the product: -2 * -4 = 8.
Step 8: According to the quadratic formula, the product of the roots (which is 8) should equal k.
Step 9: Therefore, we find that k = 8.

Quadratic Equations – Understanding the relationship between the coefficients of a quadratic equation and its roots through Vieta's formulas.
Sum and Product of Roots – Using the sum and product of the roots to find unknown coefficients in a quadratic equation.